• Oxygen has lesser negative electron-gain enthalpy than sulphur. But from sulphur onwards, the value becomes less negative up to polonium.

• Within the group, electronegativity decreases with an increase in atomic number.
  
  I don't undrstand how these two facts coincide.
  If electron gain enthalpy is the amount of energy released by an atom to gain electron, and if electronegativity is the tendency of an atom or radical to attract electrons,shouldn't the electron gain enthalpy become more negative down the group?Please make it clear to me..

you should remember that oxygen ,being the first element of the group it is very small .hence a new electron will be suffer repulsions  from other electrons present in the orbits,but as we go down the group the size increases therefore it will be more easier to take one electron.

electrongativity is the tendency of an atom to attract an electron so as we go down the group .the size increases therefore the electron density decreases,which inturn decreases the intensity of attraction towards an electron

A trend of decreasing E_ea going down the groups in the periodic table would be expected. The additional electron will be entering an orbital farther away from the nucleus. Since this electron is farther from the nucleus it is less attracted to the nucleus and would release less energy when added